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Stationarity-conservation laws for certain linear fractional differential equations

M. Klimek
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Abstract

The Leibniz rule for fractional Riemann-Liouville derivative is studied in algebra of functions defined by Laplace convolution. This algebra and the derived Leibniz rule are used in construction of explicit form of stationary-conserved currents for linear fractional differential equations. The examples of the fractional diffusion in 1+1 and the fractional diffusion in d+1 dimensions are discussed in detail. The results are generalized to the mixed fractional-differential and mixed sequential fractional-differential systems for which the stationarity-conservation laws are obtained. The derived currents are used in construction of stationary nonlocal charges.

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M. Klimek. 2001-04-18. Stationarity-conservation laws for certain linear fractional differential equations. https://doi.org/10.1088/0305-4470%2F34%2F31%2F311

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